Mathematical problems for miscible, incompressible fluids with Korteweg stresses

The equations governing the motion and diffusion of miscible liquids can be reduced to a form like the Navier-Stokes equations when the equation of state is for the density of a simple mixture. In particular, in this case, W=Cu+D⊇φ, where C and D are constant, is solenoidal. This allows one to introduce a generalized stream and diffusion function which may be useful in the study of two-dimensional problems. Problems of unidirectional shearing flows in the presence of gradients of composition are briefly considered